/* * Copyright (C) 2005 Josef Cejka * All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * - Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * - Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * - The name of the author may not be used to endorse or promote products * derived from this software without specific prior written permission. * * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ /** @addtogroup softfloat * @{ */ /** @file */ #include #include #include #include /** Multiply two 32 bit float numbers * */ float32 mulFloat32(float32 a, float32 b) { float32 result; uint64_t frac1, frac2; int32_t exp; result.parts.sign = a.parts.sign ^ b.parts.sign; if (isFloat32NaN(a) || isFloat32NaN(b) ) { /* TODO: fix SigNaNs */ if (isFloat32SigNaN(a)) { result.parts.fraction = a.parts.fraction; result.parts.exp = a.parts.exp; return result; }; if (isFloat32SigNaN(b)) { /* TODO: fix SigNaN */ result.parts.fraction = b.parts.fraction; result.parts.exp = b.parts.exp; return result; }; /* set NaN as result */ result.binary = FLOAT32_NAN; return result; }; if (isFloat32Infinity(a)) { if (isFloat32Zero(b)) { /* FIXME: zero * infinity */ result.binary = FLOAT32_NAN; return result; } result.parts.fraction = a.parts.fraction; result.parts.exp = a.parts.exp; return result; } if (isFloat32Infinity(b)) { if (isFloat32Zero(a)) { /* FIXME: zero * infinity */ result.binary = FLOAT32_NAN; return result; } result.parts.fraction = b.parts.fraction; result.parts.exp = b.parts.exp; return result; } /* exp is signed so we can easy detect underflow */ exp = a.parts.exp + b.parts.exp; exp -= FLOAT32_BIAS; if (exp >= FLOAT32_MAX_EXPONENT) { /* FIXME: overflow */ /* set infinity as result */ result.binary = FLOAT32_INF; result.parts.sign = a.parts.sign ^ b.parts.sign; return result; }; if (exp < 0) { /* FIXME: underflow */ /* return signed zero */ result.parts.fraction = 0x0; result.parts.exp = 0x0; return result; }; frac1 = a.parts.fraction; if (a.parts.exp > 0) { frac1 |= FLOAT32_HIDDEN_BIT_MASK; } else { ++exp; }; frac2 = b.parts.fraction; if (b.parts.exp > 0) { frac2 |= FLOAT32_HIDDEN_BIT_MASK; } else { ++exp; }; frac1 <<= 1; /* one bit space for rounding */ frac1 = frac1 * frac2; /* round and return */ while ((exp < FLOAT32_MAX_EXPONENT) && (frac1 >= ( 1 << (FLOAT32_FRACTION_SIZE + 2)))) { /* 23 bits of fraction + one more for hidden bit (all shifted 1 bit left)*/ ++exp; frac1 >>= 1; }; /* rounding */ /* ++frac1; FIXME: not works - without it is ok */ frac1 >>= 1; /* shift off rounding space */ if ((exp < FLOAT32_MAX_EXPONENT) && (frac1 >= (1 << (FLOAT32_FRACTION_SIZE + 1)))) { ++exp; frac1 >>= 1; }; if (exp >= FLOAT32_MAX_EXPONENT ) { /* TODO: fix overflow */ /* return infinity*/ result.parts.exp = FLOAT32_MAX_EXPONENT; result.parts.fraction = 0x0; return result; } exp -= FLOAT32_FRACTION_SIZE; if (exp <= FLOAT32_FRACTION_SIZE) { /* denormalized number */ frac1 >>= 1; /* denormalize */ while ((frac1 > 0) && (exp < 0)) { frac1 >>= 1; ++exp; }; if (frac1 == 0) { /* FIXME : underflow */ result.parts.exp = 0; result.parts.fraction = 0; return result; }; }; result.parts.exp = exp; result.parts.fraction = frac1 & ( (1 << FLOAT32_FRACTION_SIZE) - 1); return result; } /** Multiply two 64 bit float numbers * */ float64 mulFloat64(float64 a, float64 b) { float64 result; uint64_t frac1, frac2; int32_t exp; result.parts.sign = a.parts.sign ^ b.parts.sign; if (isFloat64NaN(a) || isFloat64NaN(b) ) { /* TODO: fix SigNaNs */ if (isFloat64SigNaN(a)) { result.parts.fraction = a.parts.fraction; result.parts.exp = a.parts.exp; return result; }; if (isFloat64SigNaN(b)) { /* TODO: fix SigNaN */ result.parts.fraction = b.parts.fraction; result.parts.exp = b.parts.exp; return result; }; /* set NaN as result */ result.binary = FLOAT64_NAN; return result; }; if (isFloat64Infinity(a)) { if (isFloat64Zero(b)) { /* FIXME: zero * infinity */ result.binary = FLOAT64_NAN; return result; } result.parts.fraction = a.parts.fraction; result.parts.exp = a.parts.exp; return result; } if (isFloat64Infinity(b)) { if (isFloat64Zero(a)) { /* FIXME: zero * infinity */ result.binary = FLOAT64_NAN; return result; } result.parts.fraction = b.parts.fraction; result.parts.exp = b.parts.exp; return result; } /* exp is signed so we can easy detect underflow */ exp = a.parts.exp + b.parts.exp - FLOAT64_BIAS; frac1 = a.parts.fraction; if (a.parts.exp > 0) { frac1 |= FLOAT64_HIDDEN_BIT_MASK; } else { ++exp; }; frac2 = b.parts.fraction; if (b.parts.exp > 0) { frac2 |= FLOAT64_HIDDEN_BIT_MASK; } else { ++exp; }; frac1 <<= (64 - FLOAT64_FRACTION_SIZE - 1); frac2 <<= (64 - FLOAT64_FRACTION_SIZE - 2); mul64integers(frac1, frac2, &frac1, &frac2); frac2 |= (frac1 != 0); if (frac2 & (0x1ll << 62)) { frac2 <<= 1; exp--; } result = finishFloat64(exp, frac2, result.parts.sign); return result; } /** Multiply two 64 bit numbers and return result in two parts * @param a first operand * @param b second operand * @param lo lower part from result * @param hi higher part of result */ void mul64integers(uint64_t a,uint64_t b, uint64_t *lo, uint64_t *hi) { uint64_t low, high, middle1, middle2; uint32_t alow, blow; alow = a & 0xFFFFFFFF; blow = b & 0xFFFFFFFF; a >>= 32; b >>= 32; low = ((uint64_t)alow) * blow; middle1 = a * blow; middle2 = alow * b; high = a * b; middle1 += middle2; high += (((uint64_t)(middle1 < middle2)) << 32) + (middle1 >> 32); middle1 <<= 32; low += middle1; high += (low < middle1); *lo = low; *hi = high; return; } /** @} */